Atkin-Lehner |
11+ 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
109681a |
Isogeny class |
Conductor |
109681 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-34458589451 = -1 · 112 · 136 · 59 |
Discriminant |
Eigenvalues |
1 1 1 -1 11+ 13+ -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-173,8959] |
[a1,a2,a3,a4,a6] |
Generators |
[651:3379:27] |
Generators of the group modulo torsion |
j |
-117649/7139 |
j-invariant |
L |
8.2288963926966 |
L(r)(E,1)/r! |
Ω |
0.96130950288862 |
Real period |
R |
2.1400226265309 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000052952 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
649a1 |
Quadratic twists by: 13 |